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Department of Energy Technology, Aalborg University, Denmark

Modular Multi-Level Converter:

Modeling, Simulation and Control

in Steady State and Dynamic

Conditions

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Title: Modular Multi-Level Converter: Modeling, Simulation and Control in Steady State and Dynamic Conditions Semester: WPS2 (10th) Semester theme: [] Project period: 01/02/12 to 30/05/12 ECTS: 30 Supervisor: Remus Teodorescu Luca Zarri Project group: [WPS2 1056]

_____________________________________ [Name 1]

Copies: [2] Pages, total: [83] Appendix: [] Supplements: [] By signing this document, each member of the group confirms that all group members have participated in the project work, and thereby all members are collectively liable for the contents of the report. Furthermore, all group members confirm that the report does not include plagiarism.

SYNOPSIS: The aim of this project is the analysis

of a Modular Multilevel Converter

(MMC) and the development of a

control scheme for energy stored.

The analysis is based on the use of a

simplified circuit constituted by a

single leg of the converter where all

the modules in each arm are

represented by a single variable

voltage source. Control scheme are

thus investigated, focusing on the

balancing between upper and lower

arm voltage and on the control of the

overall energy stored in converter leg.

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Preface

This work, carried out by Giacomo Casadei, is a part of the final thesis to accomplish

the Master Degree in Automation Engineering at the University of Bologna (Italy). It

started at the beginning of February 2012 at the Department of Energy Technology,

Aalborg University, and will be completed in Winter 2012 at the University of

Bologna, Department of Electrical Engineering.

Prof. Remus Teodorescu, and Prof. Luca Zarri are the supervisors of this thesis.

Aalborg, June 8, 2012

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Acknowledgements I would like to thank my supervisor Prof. Remus Teodorescu for giving me the

opportunity to be involved with such a subject that is interesting and modern. I also

would like to thank Prof. Luca Zarri for its valuable help and guidance during my

study in Automation Engineering. Their advices and comments not only helped me

for specific issues but also improved my knowledge.

Additionally the author would like to thank all colleagues met in AAU, with whom he

shared this wonderful experience and work, and all his home and Danish friends.

Last but not the least, the author would like to thank all his family for infinite support

and love.Ill never be able to give you back what you gave me.

A special thanks goes to Earth and Pillars.

Dedicated to silence.

Aalborg, June 8, 2012

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Summary

The aim of this project is the analysis of a Modular Multilevel Converter (MMC) and

the development of a control scheme for energy stored. The converter is characterized

by a modular arm structure, formed by a cascade connection of a large number of

simple chopper cells with floating DC capacitors: these cells are called Sub-Modules

(SM) and can be easily assembled into a converter for high- or medium-voltage power

conversion systems. The analysis is based on the use of a simplified circuit constituted

by a single leg of the converter, where all the modules in each arm are represented by

a single variable voltage source. The circuit model is derived as a system of

differential equations that can be used for analyzing both the steady state and dynamic

behavior of the MMC, from voltages and thus energy point of view. The converter

structure requires an arm voltage balancing control and a leg total voltage control in

order to achieve a stable behavior in all operating conditions. The validity and the

effectiveness of the voltage control strategy are confirmed by numerical simulations.

Thesis objective is to deepen control issues about MMC family of converters: in order

to approach properly control system, a state of the art analysis had to be done.

This analysis showed that, as of today, few modeling approaches have been

investigated and thus, control issues are still difficult to be solved. In fact, it became

clear that a different modeling approach will be necessary in order to solve all

dynamic operation requirements.

Following a reliable modeling approach, carried out by A. Antonopoulos, L.Angquist,

and H.P. Nee in On dynamics and voltage control of the modular multilevel

converter (European Power Electronics Conference (EPE), Barcelona, Spain,

September 8-10, 2009), dynamic behavior of converter voltages and energy has been

analyzed.

New and improved regulators have been implemented: in fact, in order to solve

dynamic transients of the MMC (for instance LVRT, Failure Mode condition etc.) it

became clear that conventional control structures are not sufficient.

The over mentioned modeling approach leads to a highly non-linear system: non-

linearity is present also in the input, thus advanced control approach are difficult to be

implemented.

Thus, in the fifth chapter of this thesis, a new modeling approach is proposed, aiming

to simplify advanced control implementation.

It can be concluded, that with the new modeling approach a significant contribution to

control issues will be possible.

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Thesis Layout Chapter I

1. Introduction and Motivations

1.1. Objectives

1.2. Limitations

Chapter II

1. Description and Operation Principle of MMC

Chapter III

1. Mathematical Model of the MMC

2. Control Strategy

3. Consideration About Control Strategy And Model

Chapter IV

1. Development of a MATLAB model

2. First Model: Converter Operation and Model Verification

3. Second Model: Energy Control:

3.1. Simulation Results

4. Third Model: Output Power Control:

4.1. Simulation Results

5. Fourth Model: Mega-Watt System

5.1. Capacitance Relationship with Voltage Ripple

5.2. Simulation Results

5.3. Simulation Results: Sub-Modules Failure Mode

5.4. Simulation Results: LVRT

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Chapter V

1. Motivations for a New Modeling Approach

2. Modeling Principles and Equations

3. Control Proposal

4. Future Works

Chapter VI - Conclusions

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List of symbols First Model

: sub-modules capacitor

: number of sub-modules in each arm

: total capacitance of the arm

: equivalent capacitance of the arm m

: arm impedance

: general modulation index

: m arm voltage

: voltage stored in arm capacitor

: current flowing through the arm

: upper and lower arm currents respectively

: output current

: differential current

: upper and lower sub-modules voltages respectively

: upper and lower modulation indexes respectively

: DC voltage

: output voltage

: modulation carrier, with as pick value

: upper and lower arm voltages respectively

: differential voltage

: internal alternating voltage

: total energy stored in upper and lower sub-modules respectively

: total energy stored in one phase and difference between upper and lower

energy

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: grid voltage

: line impedance

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List of symbols Second Model

: upper and lower arm voltages respectively

: output voltage

: upper arm impedance

: lower arm impedance

: upper and lower arm currents respectively

: output current

: DC voltage

: upper and lower modulation indexes respectively

: upper and lower arm capacitor voltages

: upper and lower arm equivalent capacitor

: upper and lower arm reference currents

: output current reference

: differential current reference

: upper and lower modulation indexes reference respectively

: upper and lower arm voltages reference respectively

: total energy stored in the arm and difference between upper and lower arm

energy

: total energy and difference of upper and lower arm energy references

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Chapter I

1 Introduction and Motivations

The development of new technologies and devices during the 20th

century enhanced

the interest in electric power systems. Modern civilization based his operation on an

increasing energy demand and on the substitutions of human activities with complex

and sophisticated machines; thus, studies on electric power generation and conversion

devices become every day more and more important.

The recent attention in environment protection and preservation increased the interest

in electrical power generation from renewable sources: wind power systems and solar

systems are diffusing and are supposed to occupy an increasingly important role in

world-wide energy production in coming years.

Not only house utilities, but industrial applications and even the electrical network

requirements display the importance that energy supply and control will have in the

future researches.

As a consequence, power conversion and secondly control is required to be reliable,

safe and available in order to accomplish all requirements, both from users and legal

regulations, and to reduce the environmental impact.

Voltage Source Converter (VSC) technology is becoming common in high-voltage

direct current (HVDC) transmission systems (especially transmission of offshore

wind power, among others). HVDC transmission technology is an important and

efficient possibility to transmit high powers over long distances.

The vast majority of electric power transmissions were three-phase and this was the

common technology widespread. Main advantages for choosing HVDC instead of AC

to transmit power can be numerous but still in discussion, and each individual

situation must be considered apart. Each project will display its own pro and con

about HVDC transmission, but commonly these advantages can be summarized:

lower losses, long distance water crossing, controllability, limitation short circuit

currents, environmental reason and lower cost.

One of the most important advantages of HVDC on AC systems is related with the

possibility to accurately control the active power transmitted, in contrast AC lines

power flow cant be controlled in the same direct way.

However conventional converters display problems into accomplishing requirements

and operation of HVDC transmission. Compared to conventional VSC technology,

Modular Multilevel topology instead offers advantages such as higher voltage levels,

modular construction, longer maintenance intervals and improved reliability.

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Figure 1 - ABB DolWin Installation, using HVDC connection

A multilevel approach guarantees a reduction of output harmonics due to sinusoidal

output voltages: thus grid filters become negligible, leading to system cost and

complexity reduction.

Like in many other engineering fields, modular and distributed systems are becoming

the suggested topology to achieve modern projects requirements: this configuration

ensure a more reliable operation, facilitates diagnosis, maintenance and

reconfigurations of control system. Especially in fail safe situations, modular

configuration allows control system to isolate the problem, drive the process in safe

state easily, and in many cases allows one to reach an almost normal operation even if

in faulty conditions.

However, it is necessary to take into account also disadvantages brought by Modular

design: the control scheme actually results more complex and requires a two level

configuration. Each modular part as to be controlled independently, but a master

control layer is needed to reach the overall system behaviour requirements. It is

necessary to provide a proper division of tasks between local controllers and master

controller: must of all, the communication system becomes really important in order

to achieve overall stability and time deadline accomplishment.

In the case of MMC, the concept of a modular converter topology has the intrinsic

capability to improve the reliability, as a fault module can be bypassed allowing the

operation of the whole circuit without affecting significantly the performance.

Many multi-level converter topologies have been investigated in these last years [1],

having advantages and disadvantages during operation or when assembling the

converters. To solve the problems of conventional multi-level converter a new MMC

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topology was proposed in [2]-[5], describing the operation principle and performance

under different operating conditions. A simple schematic of this converter with N

modules per arm is shown in Fig. 1. The MMC proposed in [2]-[5] is one of the most

promising power converter topology for high power applications in the near future,

particularly in HVDC links (e.g. transmission of offshore wind power, among others).

Siemens has a plan of putting this converter into practical applications with the trade

name HVDC-plus. The system configuration of the HVDC-plus has a power of 400

MVA, a dc link voltage of 200 kV, and each arm composed of 200 cascaded chopper

cells [6].

This converter topology has been investigated by several research teams lately [7]-

[12]. These papers where mainly focused on the analysis of simplified circuit models

and improved control systems to achieve a reliable and stable operation of the

converter, as the cascaded connection of multiple sub-modules in each arm and leg

requires the voltage balance among the several sub-modules of each arm and between

upper and lower arms. The control of the total leg voltage and differential voltage

between upper and lower arms is a crucial point as it can affect seriously the operation

of MMC if not properly implemented. The potential interaction between these two

loops of control will be deepened and discussed; it will be important to evaluate the

possibility of control task distribution; this analysis is required to design the most

suitable control scheme.

The aim of this paper is to accomplish the stable voltage control of the MMC in all

operating conditions and the theoretical analysis is based on the circuit model

proposed in [8], hence, the same terminology will be used. The approach is based on

using a continuous model, where all modules in each arm are represented by variable

voltage sources, and PWM effects are neglected. The numerical simulations of the

converter show the presence of high currents that can circulate through the phase legs,

leading to the need of over-rating the modules. Besides to this, the presence of these

currents produces an energy transfer between the arms, leading to possible

instabilities of the converter. A suitable control strategy has been implemented for

avoiding instabilities in all operating conditions. The validity and the effectiveness of

the voltage control strategy is confirmed by numerical simulations.

1.1 Objectives In this thesis, analysis, modeling and control of a 13 MW/20 KV MMC converter are

investigated. Thus, objectives can be summarized:

MMC operation principles: state of art and actual achievement

MMC modeling: analysis of modeling approaches available

Modeling Development and Simulation Verification of a KW system

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Modeling Development and Simulation Verification of a MW system

Control Strategies Analysis and Implementation: firstly on the KW system,

then applied and verified on the MW system

New proposal for modeling and control

1.2 Limitations This thesis main objective is to find a performing control system for the energy stored

in the converter: even if MMC is a well-known topology of converter, few modeling

and control approach are available.

To carry out this primary analysis, a modeling approach has been chosen and

followed, and can be found in [8]: this approach showed to be the most promising,

both for the analysis of MMC operation and for the development of control structure.

However, in Chapter V of this thesis a new modeling approach is suggested, in order

to simplify control strategy study.

Being the energy monitoring and control the aim of this project, modeling neglects

low level operation and dynamics of the system: sub-modules are simplified with an

equivalent variable voltage source, ideally controlled.

This assumption, gives the opportunity to study the system from a proper point of

view in terms of energy: on the other side, sub-modules operation is hidden and all

issues connected are not dealt in this thesis.

A different approach should be investigated, in order to account also sub-modules

operation in the modeling and through this, in control strategy development.

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Chapter II

1- Description and principle of operation of MMC

The typical structure of a MMC is shown in Fig. 2, and the configuration of a Sub-

Module (SM) is given in Fig. 3. Each SM is a simple chopper cell composed of two

IGBT switches (T1 and T2), two anti-parallel diodes (D1 and D2) and a capacitor C.

Each phase leg of the converter has two arms, each one constituted by a number N of

SMs. In each arm there is also a small inductor to compensate for the voltage

difference between upper and lower arms produced when a SM is switched in or out.

Figure 2 - Schematic of a three-phase Modular Multi-level Converter

With reference to the SM shown in Fig. 2, the output voltage UO is given by,

UO = UC if T1 is ON and T2 is OFF

UO = 0 if T1 is OFF and T2 is ON

where UC is the instantaneous capacitor voltage.

The configuration with T1 and T2 both ON should not be considered because it

determines a short circuit across the capacitor. Also the configuration with T1 and T2

both OFF is not useful as it produces different output voltages depending on the

current direction. Fig. 4 shows the current flows in both useful states.

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In a MMC the number of steps of the output voltage is related to the number of series

connected SMs. In order to show how the voltage levels are generated, in the

following, reference is made to the simple three level MMC configuration shown in

Fig. 5.

Figure 3 Chopper cell of a Sub-Module

Figure 4 - States of SM and current paths

Inverse current flow

Direct current flow

T1 D1

C

UO T2 D2

UC

T1 OFF - T2 ON

SM off-state

T1 ON - T2 OFF

SM on-state

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Figure 5 - Schematic of one phase of Three-Level Converter

In this case, in order to get the positive output, +UD/2, the two upper SMs 1 and 2 are

bypassed. Accordingly, for the negative output, - UD/2, the two lower SMs 3 and 4 are

bypassed. The zero state can be obtained through two possible switch configurations.

The first one is when the two SMs in the middle of a leg (2 and 3) are bypassed, and

the second one is when the end SMs of a leg (1 and 4) are bypassed. It has to be noted

that the current flows through the SMS that are not by passed determining the

charging or discharging of the capacitors depending on the current direction.

Therefore, in order to keep the capacitor voltages balanced, both zero states must be

used alternatively. The voltage waveform generated by the three level converters is

shown in Fig. 6.

Figure 6 - Voltage waveform of a Three-Level Converter

UD /2

UD /2

+UD /2

-UD /2

VAC

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The principle of operation can be extended to any multi-level configuration as the one

represented in Fig. 7.

Figure 7 - Schematic of one phase of Multi-Level Converter

In this type of inverter, the only states that have no redundant configurations are the

two states that generate the maximum positive and negative voltages, + UD/2 and

UD/2. For generating the other levels, in general there are several possible switching

configurations that can be selected in order to keep the capacitor voltages balanced. In

MMC of Fig. 6, the switching sequence is controlled so that at each instant only N

SMs (i.e. half of the 2N SMs of a phase leg) are in the on-state. As an example, if at a

given instant in the upper arm SMs from 2 to N are in the on-state, in the lower arm

only one SM will be in on-state. It is clear that there are several possible switching

configurations. Equal voltage sharing among the capacitor of each arm can be

achieved by a selection algorithm of inserted or bypassed SMs during each sampling

period of the control system. A typical voltage waveform of a multi-level converter is

shown in Fig. 8.

Figure 8 - Voltage waveform of a Multi-Level Converter

UD /2

UD /2

+UD /2

-UD /2

VAC

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Chapter III 3.1 - Mathematical model of the MMC

The typical structure of an MMC, shown in Fig. 1, can be summarized into 3 levels:

I. sub-modules SM (the lower level, usually Chopper cells)

II. arm (second level of the converter, half of the leg-phase)

III. leg (can be considered one phase)

If a two-level control structure is considered, for instance a Master-Slave structure,

lower level of control is assigned to sub-models (level I), instead upper level of

control deals with arm-leg voltage and currents control (level II, III). It is assumed

that a lower level control for the sub-modules is present ensuring that all capacitors

are equally charged.

As suggested in [13], most of existing investigations and simulations are based on

switched or discrete models. However, discrete models have two main disadvantages:

a) discrete models do not allow an analytical approach to model the converter

and to design the control system;

b) numerical solution of complex converter configurations using a high number

of SMs require considerable simulation time.

A continuous model can overcome these disadvantages. Therefore, to clearly

understand the operation of this converter it is necessary to write the voltage-current

equations and to determine a continuous model suitable to design a control scheme.

In the following, an analysis is carried out with the aim to control the upper and lower

arm voltages, using the continuous model presented in [8], that considers only one

converter phase and is based on time-variable capacitors.

Considering a converter with N sub-modules per arm, each arm can be controlled with

an insertion index (modulation index) n(t), where n(t)=0 means that all sub-modules

in the arm are by-passed, on the other side n(t)=1 means that all the sub-modules in

the arm are inserted.

Ideal capacitance of the arm should be:

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The effective capacitance of the arm is dependent on the insertion index, so it can be

written as:

where the m apex means the number of the arm (for instance, in a three-phase

converter m=1,2,3,..,6).

It would be possible to have a full representation of the MMC converter, including

operation of each sub-module, but this approach tends to be fairly complicated and

not easy to be used as a base for control schemes development.

A simpler way would be to consider a continuous model, but 2 important assumptions

are necessary in order to develop this approach:

1. the switching frequency is much higher than the frequency of the output

voltage

2. the resolution of the output voltage is small, compared to the amplitude of the

output voltage (i.e. high number of sub-modules)

Assuming 1 and 2, its possible to create a continuous model which represents the

overall operation of the converter, neglecting the single sub-modules behaviour: this

type of model is suitable for control system design and makes it possible to focus on

the energy stored in the converter and its balance between arms. The simplified model

is shown in Fig. 9.

Figure 9 - Simplified Circuit Used for the Analysis

UD/2

UD/2

Carm ucu

Carm ucu

Zarm

Zarm

iU

iL

iV

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Again, apex m represent the arm, n(t) is the insertion index, instead uc(t) is the sum

of all capacitance voltage in the m arm. Then equations (3) and (4) follow.

With reference to Fig. 8, where only one phase is considered, it is possible to write a

set of equations for currents: currents from upper and lower arms, rispectively iU and

iL, will constitute the output current iV.

The idiff current represents the current that circulates from the phase leg to the DC link

(and/or to another phase leg).

}

These equations are representing the ideal condition in wich the contributions of

upper and lower arms to the output current are equal. The difference current is

introduced to consider the possible situation in which the capacitors are not equally

charged to the reference value. In this MMC configuration the sum of all capacitor

voltages of one arm is assumed to be equal to the DC Voltage uD.

Equations (6) and (7) are the same of (4), just emphasizing the contributions of upper

and lower arms in terms of voltage and current.

With all these equations and the semplified circuit shown in Fig. 8, it is possible to

write equations (8) and (9) as simple Kirkhoff voltage equations.

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Subtracting equation (9) to (8), and substituting the following equations

it is possible to obtain this dynamic equation of the current idiff :

From equations (6) and (7), substituting iU and iL with the expressions given in (5),

two dynamic equations of upper and lower arm voltages are obtained:

From (12) it can be noted that with idiff equal to zero, the load current acts in order to

unbalance the upper and lower arm voltages. In steady state conditions the load

current is changing assuming positive and negative values, then, the time derivative of

the arm voltages are also changing, and in ideal conditions the arm voltage should

oscillate around a constant mean value. The presence of non idealities and losses may

lead the converter to be unstable. As a consequence, it can be concluded that only the

presence of a suitable difference current allows the converter to operate correctly.

Using (11) and (12), a dynamic and continuous model is thus obtained and shown in

(13).

[

]

[

]

[

]

[

]

Assuming that a sinusoidal output voltage is desired, the reference signal for

modulation is

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and the ideal terminal voltage is given by

In order to solve the system of equations (13) the load current should be known. Here,

the following alternating current is assumed as the output load current

Where is the load phase angle and is arbitrary.

Using the reference signal in (14), the modulation indices for upper and lower arms

can be expressed as

It can noted that the sum of upper and lower modulation indexes is always equal to 1.

As a consequence, assuming the capacitor voltages of all modules equal to the

refernce value, the sum of the voltages of upper and lower arms is always equal to the

DC voltage uD.

In real operating conditions the capacitor voltages will not be exactly equal to the

reference value and as a result a difference voltage will be present forcing a difference

current to flow between the leg and the DC source. A suitable control of this current is

crucial for achieving a correct operation of the converter and an equal sharing of the

DC voltage among all modules.

A possible control strategy is the one based on adding an offset voltage to upper and

lower arm voltages uCU and uCL defined trough (17) and (18). This offset voltage (udiff)

is determined with some criteria aimed to keep the module voltages as close as

possible to the reference value or to keep the energy stored in upper and lower

capacitors equalized.

It will be shown in the next section that udiff will not affect the terminal voltage (as uV

is related to the difeerence between upper and lower arm voltages), but will impact on

idiff current instead.

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The number of levels that can be obtained depends on the assumptions made for the

analysis. When assuming a constant DC voltage, actually it is possible to generate

output voltages having a number of levels equal to 2N+1, whereas the number of

levels must be reduced to N+1 if the the DC voltage has to be kept under control by

the converter itself.

This is the situation that occurs in HVDC systems composed by two MMCs

connecting the two ends of a DC cable. In this case there is no DC capacitor between

the DC voltage terminals and a DC voltage controller is necessary. In this analysis a

constant DC voltage will be assumed as the aim is to develop a strategy for keeping

under control the total energy stored in each leg and the unbalance between the energy

stored in upper and lower arms.

3.2 - Control Strategy

By adding and subtracting equations (9) to (8), it is possible to obtain two equations

that clearly explain a possible approach to MMC control:

As suggested in [8], from (19) and (20) is possible to draw the following conlcusion:

the output voltage uv depends only on the current iV and on the difference

between upper and lower voltage uCU, uCL

the arm voltage difference acts like an inner alternating voltage, R and L as a

passive inner impedence for alternating current

idiff depends only on the DC link voltage and the sum of arm voltages

Therefore it is possible to note that adding the same quantity to both arm voltages will

not affect the AC side, but will influence the difference current instead, wich can thus

be controlled.

It is opportune for control purposes to obtain an expression of upper and lower arm

voltages in wich this voltage difference is included. Starting from (8) and substituting

the upper current with

31

leads to

(21) can be rewritten as

Considering that form (19)

(22) can be rewritten as

The same development can be carried out for uCL yielding

where udiff is defined as

Equations (24) and (25) show how the difference voltage contribute to the reference

values of upper and lower arm voltages.

The quantity ev defined as

32

is practically representing the output voltage uv, apart from the voltage drop across R

and L as shown in (19). So, in the following, ev is used to represent the output voltage

uv.

In order to determine a possible control strategy for determining udiff , it is opportune

to introduce the energy stored in upper and lower arm capacitors.

Assuming that voltage and thus energy stored in each arm is equally shared between

sub-modules, the upper and lower energy are

[

(

)

]

[

(

)

]

Considering now power equations of both upper and lower arms, it is possible to

write:

(

) (

)

(

) (

)

The total capacitor energy in the leg and the difference capacitor energy between

upper and lower arms are

Differentiating (32) and (33), and introducing (30) and (31) yields

( )

(

)

33

These equations are very important to discuss the influence of idiff on the total and

difference capacitor energies. From (34), assuming idiff having only a dc component its

product with uD represents the power delivered to the ac side (load and capacitors).

The quantity udiff idiff represents the losses on the arm resistance R and the magnetic

energy variation in the arm inductance L, is the load power. So, a DC component

of idiff can be used to control the total capacitor energy.

From (35), it can be noted that a DC component of idiff has no impact on the difference

capacitor energy as there are no dc components in ev. The conclusion is that the DC

component of idiff can only be used for controlling the total capacitor energy stored in

the converter leg.

On the other hand, an alternating component of idiff, having the same fundamental

frequency as the output voltage ev, could be usefully employed to control the

distribution of the capacitor energy between upper and lower arms. In fact, the

product ev idiff has a dc component that can be used to force the energy difference to

change. A similar effect is created by udiff iV, but this quantity should be smaller for

small value of R and L, thus in the following the control strategy will be developed

with reference to the quantity ev idiff only.

3.3 - Consideration about Control Strategy and

Model

It is necessary to make an important remark: the equations wrote and discussed in

previous section lead to a continuous model, suitable for analysis and understanding

of operation principle of the MMC. On the other hand, from the control point of view,

these equations are not easy to use: even if it is possible to decouple continuous and

alternate component of differential current, in order to properly track references, non-

linear couplings make really complex advanced control structures.

From equations (34) and (35) it becomes clear that the input variables, or rather

modulation indexes, influence dynamics of the energy as a non-linear input: in fact,

the modulation indexes directly influence differential voltage, and the relationship

between differential voltage and differential current is a low-pass filter (Fig. 10).

Figure 10 - Input Control Relationship

34

Neglecting this low pass filter it is possible to consider that input variables are a

square input for the system: this condition makes more difficult the development of

advanced control strategies and the study of complex control strategies.

Thus, a different approach in the modeling will be developed in order to simplify the

analysis from the control point of view: this modeling approach will be deepened in

Chapter V.

The control strategy implemented is a linear control which aims to operate in the

proximity of the region where the control can be considered linear: actually, control

input will be limited in order to preserve this assumption. Otherwise, the non-linear

input of the control can affect operation of the system, leading to instability.

Two different loops will be implemented, the first one to control the overall energy of

the MMC leg, the second to control the balance between upper and lower arms of the

phase-leg.

The interaction between two loops may lead to instability: because of the non-linear

configuration of system equations, it is hard to analyze systems coupling properly (for

instance Relative Gain Array analysis).

It is however evident that total energy and energy balance interact dynamically in

system operation: in order to make a decoupling, balance of energy loop is tuned in

order to be greatly slower than the overall energy loop. This frequency decoupling

will highly benefit differential current waveform: if not performed, overall energy and

balance interaction leads to a really distorted differential current. This current,

flowing in the phase-leg, would produce a voltage drop on the phase impedance,

increasing losses and disturbances in the stability of the system.

Then, an output current control loop will be implemented in order to simulate the

operation of the converter in all different possible conditions. The general block

diagram of control scheme is shown in Fig. 11.

35

Figure 11 - Control Scheme, Block Diagram

36

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Chapter IV

4.1 - Development of a MATLAB model

Starting from equations and discussions of Chapter III, it is possible to define a simple

dynamic model of one phase of the converter.

Below are listed the chosen equations:

[

]

[

]

[

]

[

]

(

) (

)

(

) (

)

Equation (36) is the output voltage equation, where ug is the grid voltage, and Rg, Lg

the parameters of the line connecting MMC to the grid.

The previous equations are implemented on Simulink, with the use of Embedded

MATLAB Functions.

38

4.2 - First model: Converter Operation and Model

Verification

The first system implemented in MATLAB-Simulink includes only the equations in

(13), but it is however important to understand the operation of the converter: in

particular, the necessity of controlling the differential current and thus the energy

stored in upper and lower arm becomes clear.

In this simulation, output voltage and current are imposed and the operation of the

system is then observed: modulation indexes are calculated ideally, using equations

(24) and (25), neglecting differential voltage usage (no control strategy is

implemented yet) and neglecting also the voltage drop of the output current on the

arm parameters (i.e. ).

Figure 12 - First Model MATLAB Scheme

MATLAB Model Implementation can be seen in Fig. 12.

Green blocks implement model equations; the red block instead contains the

calculation of the modulation indexes: in the right bottom, output voltage and current

are imposed, assuming a load-phase angle equal to zero.

[nu]

u_cu1

[u_cu]

u_cu

[nl]

u_cl1

[u_cl]

u_cl

m(t)

[i_diff]

i_diff

nu

nl

u_cu

u_cl

U_arm

fcn

U_arm Calculation

with U_CL,U_CU and

Modulation Indexes

i_dif f

nu

nl

i_v

U

fcn

U_CU & U_CL

Scope5

Scope4

Scope3

Scope2

Scope1

Scope

Output Current (pi/36 phase)

1

s

Integrator2

1

s

Integrator1

1

s

Integrator

i_v

i_dif f

Ifcn

I_u & I_l

i_dif f

nu

nl

u_cu

u_cl

i_dif f _der

fcn

I_DIFF

[i_l]

Goto5

[i_u]

Goto4

[u_arm_low]

Goto3

[u_arm_up]

Goto2

[u_v]

Goto1

[i_v]

Goto

Ud/4

Gain6

[i_v]

From9

[u_cu]

From8

[nu]

From7

[i_diff]

From6

[nl]

From5

[nu]

From4

[nl]

From3

[nu]

From2

[u_v]

From18

[u_cl]

From15

[u_cu]

From14

[u_cl]

From13

[u_cu]

From12

[u_cl]

From11

[nl]

From10

[i_v]

From1

[i_diff]

From

u_v

u_cu

u_cl

u_dif f

nu

nl

Control System

39

The upper green block represents the dynamic of differential current; the middle green

block represents the capacitor voltage dynamic, the lower block calculates the upper

and lower arm voltage, multiplying the capacitor voltage by the modulation index. On

the right side, the green block is used to calculate the upper and lower arm current.

Output voltage and current, and other system parameters are listed below in Tab. 1.

Tab. 1 List of system parameters

It is important to underline that the model implemented is a kW system: the choice to

preliminary study a smaller system, compared with the final objectives of project, is

motivated by control issues and parameters availability.

It will be shown that control strategy implemented is almost independent from

parameters changes; however it is easier to start solving the problem from a small

scale system. Furthermore, parameters for a kW system were available from the

beginning of the project, instead MW parameters required some time and deepening

to be confirmed.

No control loop is implemented yet, and the converter is not able to keep the capacitor

voltage to the initial value, i.e. the capacitor voltage decreases from the initial value to

a non-desired steady state condition, the same happens to differential current.

Arm voltages waveforms are shown in Fig. 13.

After a brief transient the differential current acts in order to maintain the capacitor

voltage stable (waveform in Fig. 14), and the system is operating properly.

In order to control the capacitor voltage and thus totla energy stored in upper and

lower arm, and their balance, a control on the differential current must be

implemented.

40

Figure 13 Upper (Blue) and Lower (Green) Arm Capacitance Voltage (V):

without control loop

Figure 14 - Differential Current Waveform (A): without control loop

0 1 2 3 4 5 6 7 8 9 10130

140

150

160

170

180

190

200

210

Time

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

Time

Time (s)

Time (s)

41

4.3 - Second model: Energy Control

The second system implemented includes energy equations (30) and (31) and propose

an energy control strategy, to obtain a stable single-phase leg of the converter: to

accomplish this, differential current is used. Like the previous model, output voltage

and current are still imposed and the operation of the converter-leg is consequently

observed and controlled.

As deducted by equations (19) and (20), differential current can be controlled by a

differential; this voltage will not affect the AC (output) side (i.e. adding the same

quantity to upper and lower arm voltage does not change the output current or

voltage, but imposes a differential current to flow in the phase-leg).

Thus, a simple but efficient control strategy controls overall energy stored and the

balance between upper and lower arm energy through the differential current, using

the differential voltage as intermediate control input: in fact this differential voltage,

sum of two different control components, will modify modulation indexes, changing

the ideal value calculated assuming constant the capacitor voltages.

Figure 15 - Second Model MATLAB Scheme

Controlling The Overall Energy Stored In the Converterand The Balance of Energy

w_cl

w_cl

[nu]

u_cu1

u_cu

u_cu

[nl]

u_cl1

u_cl

u_cl

m(t)

i_diff

i_diff

u_arm_up

u_arm_low

i_dif f

i_v

W

fcn

W_CU & W_CL

w_cu

W-cu

nu

nl

u_cu

u_cl

U_arm

fcn

U_arm Calculation

with U_CL,U_CU and

Modulation Indexes

i_dif f

nu

nl

i_v

U_der

fcn

U_CU & U_CL

Scope9

Scope8

Scope7

Scope6

Scope5

Scope4

Scope3

Scope2

Scope12

Scope11

Scope10

Scope1

Scope

Output Current (pi/36 phase)1

s

Integrator3

1

s

Integrator2

1

s

Integrator1

1

s

Integrator

i_v

i_dif f

Ifcn

I_u & I_l

i_dif f

nu

nl

u_cu

u_cl

i_dif f _der

fcn

I_DIFF

[i_l]

Goto5

[i_u]

Goto4

[u_arm_low]

Goto3

[u_arm_up]

Goto2

u_v

Goto1

i_v

Goto

Ud/4

Gain6

i_v

From9

u_cu

From8

[nu]

From7

i_diff

From6

[nl]

From5

[nu]

From4

[nl]

From3

[u_arm_up]

From21

[u_arm_low]

From20

[nu]

From2

i_v

From19

i_diff

From17

u_cl

From15

u_cu

From14

u_cl

From11

[nl]

From10

i_v

From1

i_diff

From

nu

nl

Control System

42

Dynamic equations for upper and lower energy are implemented in the lower, right

side MATLAB Embedded block: then, the sum of the two energies stored in upper

and lower arms is the overall energy and a constant reference value is imposed. The

difference of upper and lower arm energies is used to control the balance between

upper and lower arm; thus, the reference value is set to zero. The control scheme

block is then explained and can be seen in Fig. 16.

Red blocks implement the overall energy loop: a PD controller works on the total

energy error, with the purpose of deleting the error between energy reference and the

energy effectively stored in the phase-leg.

However, being all the imposed output signals sinusoidal, there will be a steady state

error in the overall energy: the goal is to reduce this error as much as possible and to

have a fast dynamic response in case of change reference.

Green blocks implement the balance control between upper and lower arm: it is again

a PD controller, but this time a low pass filter is also required, in order to have a

stable and smooth loop. The control action generated by this loop is then multiplied

by a carrier, with the same frequency of the output signals and the impedance arm

phase.

From equations (34) and (35), rewritten in the following for convenience, it is

possible to understand how to control properly the overall energy and the energy

balance.

( )

(

)

In equation (34), differential current multiplies the DC voltage, so a DC component of

differential current is used to control the overall energy stored.

In equation (35), differential current multiplies the output voltage ( can be

considered the same of output voltage, neglecting the voltage drop of output current

on arm parameters), so an AC component of differential current is used in order to

control the balance between upper and lower energy (using the carrier technique

implemented by the yellow block).

The two control components are added and then used as a differential voltage

reference which will be followed by changing upper and lower modulation indexes,

driving the necessary differential current to control the system energy: modulation

indexes are calculated dividing the upper and lower voltage (calculated with equations

(24) and (25)) by the capacitor voltage reference, as it is shown in the lower part of

the control scheme with green blocks.

43

Figure 16 Control Scheme Implementation in MATLAB

44

An important consideration must be performed: both loops implemented to control

energy behavior include saturation. There are two important reasons in order to

impose these limitations:

Stability of the System: it is necessary to leave the control enough slack in

order to properly act on the system. It is however important to remember the

non-linear configuration of the input, which impose a strict constraint to input

magnitude

Output Tracking: this point will be shown clearly in the following model,

Chapter 4.4, where output variables control is implemented. It is important to

use a small percentage of voltage available to control energy: the remaining

part is necessary to control the output.

4.3.1 - Simulation Results

Imposing the output current, the overall energy stored in one phase leg has a brief

transient after which it oscillates around the steady state reference value: the

amplitude of the oscillation is less than 1% and the frequency is the same of the

output signals. The waveform is shown below, in Fig. 17.

Figure 17 - Overall Energy Stored in the Converter Phase (Joule): steady-state condition

of the overall energy in a converter phase

0 1 2 3 4 5 6199

199.5

200

200.5

201

201.5

TimeTime (s)

45

Initial transient is caused by the difficulty in finding a proper initial condition for the

system: even if the capacitors are charged, also differential current has to be set to a

proper value. Even if the mean value can be found, the alternate component of the

differential current in order to balance energy/voltages requires a transient.

The energy difference between upper and lower arm has a similar behavior: after a

brief transient, it reaches a steady state oscillation around the reference, 1% of

amplitude compared to the overall energy value and with the same frequency of the

output (Fig. 18).

Figure 18 - Difference Between Upper and Lower Arm Energy (Joule): steady-state

condition of the difference energy

The steady state behavior is stable as expected: some problems may occur, especially

if dynamic changes of the energy are imposed.

In these cases, transient with oscillations are present and they will be discussed and

deepened in coming sections.

0 1 2 3 4 5 6-3

-2

-1

0

1

2

3

4

5

6

TimeTime (s)

46

4.4 - Third model: Output Power Control

With the third implemented model, the goal is to deepen the behavior of the converter

about the output current control: proved the overall and balance energy control

stability, it is now possible to introduce the control of the output current.

To track the output current, a resonant controller is used; a standard PI structure

would be insufficient to cancel the sinusoidal error, so a different approach is

necessary to be adopted. The resonant controller is the most suitable for a single-

phase system: however, considering the three-phase general structure, a D-Q or Space

Vector transform will be chosen for the control structure, in order to simplify the

complexity of control loops.

A MATLAB Embedded block is added in order to implement the output current

dynamic equation; then, a resonant controller is applied to output current error, as it is

shown in Fig. 19. The controller is composed of two main contributions: a

proportional, and a resonant part. The Bode diagram is shown below in Fig. 20. The

resonant peak is in correspondence of the frequency of the output and can be changed

dynamically in order to follow different outputs (in terms of frequency).

Figure 19 - Resonant Controller MATLAB Scheme

Figure 20 - Bode Diagram of Resonant Controller

e_v_ref

1

TF 1

Ki _i_r.s

s +omega 22

Kp

Kp_i_r

i_v_err

1

45

50

55

60

65

70

75

Magnitu

de (

dB

)

102.41

102.43

102.45

102.47

102.49

102.51

102.53

102.55

102.57

102.59

-180

-135

-90

-45

0

Phase (

deg)

Bode Diagram

Frequency (rad/s)

47

The output of the resonant controller is a reference for the inner alternate voltage ,

which again will be achieved through the control of modulation indexes.

The general scheme implemented in MATLAB for the third model is represented in

Fig. 21.

Figure 21 - Third Model MATLAB Control Scheme

48

4.4.1 - Simulation Results

Simulation results show that adding control loop for the output current does not

impact the energy behavior of the system.

Both overall energy and the balance between upper and lower arm behave as shown in

previous examples: thus, it is possible to consider that energy control and output

current control are decoupled. This is possible because of saturation imposition:

actually, limitations and constraints on differential voltage are important both for

stability of the system and output variables tracking.

If tuned properly, the energy control system will use a small fraction of the DC

voltage; the remaining part is used to guarantee the output tracking. Differential

current control exploits only a small quantity of the voltage available; the rest is used

to control the output.

If the trade-off between the energy control and output power control is properly tuned,

energy loop and output loop can be considered decoupled.

Fig. 22, shows the behavior of differential current; the current has a DC component of

1.1 A, and an alternating component around 0.1 A of amplitude.

Figure 22- Differential Current Waveform (A)

0 1 2 3 4 5 60.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

TimeTime (s)

49

The error of the output current is shown in Fig. 23; it is possible to see that, after a

brief transient, the current reaches almost the desired value with an error less than 1%

of the steady state value of the output current.

Figure 23 - Output Current Error (A)

Figure 24 - Zoom of Output Current Error (A)

0 1 2 3 4 5 6-5

-4

-3

-2

-1

0

1

Time

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-0.4

-0.3

-0.2

-0.1

0

0.1

Time

Time (s)

Time (s)

50

Fig. 24 shows a zoom of the fast transient of output current error, almost impossible

to be seen in Fig. 23. The initial error is of course big (the output current starts form a

null value), but after few milliseconds the error is less than 1% of the steady state

value.

The dynamic behavior of the system needs to be investigated. To this aim, a dynamic

change of the overall energy is imposed in order to show the behavior of the system.

The imposed change is not connected to any particular working situation; it is just

used to show the dynamic response in time and damping, obtained with the control

system. For instance, this increase of the overall energy may be related to a failure

mode condition, considering the increase of energy a way to maintain the system

stable even if a certain part of the converter is not working properly.

Simulation results, illustrated in Figs. 25 and 26, show the behavior in case of a

simple proportional regulator: actually, is not a usually accepted operation response in

dynamic systems. Even if the response itself is fast, the damping obtained with a

proportional controller is not satisfying, especially in the overall energy control loop.

These results call for a PD configuration of the controller: adding a derivative action,

enough phase margin can be reached, in order to smooth the oscillation of the system.

Figure 25 - Dynamic Response of Overall Energy Stored in Phase Leg (Joule): transient

generated by a step-change in the overall energy reference

0 1 2 3 4 5 6180

200

220

240

260

280

300

TimeTime (s)

51

Figure 26 - Dynamic Response of the Difference between Upper and Lower Arm Energy

(Joule): overall energy oscillations affect also the balance loop

Derivative action is underlined with red background in Fig. 27 and simulation results

are shown in Figs. 28 and Fig. 29. Energy behavior improvements are evident and the

control system now works as expected.

Figure 27 - Addition of Derivative Action in the Controller

0 1 2 3 4 5 6-6

-4

-2

0

2

4

6

Time

u_diff _tot

1

TF 1

s+D_zero

s+D_polo

Saturation 3

Saturation 2Kp

Kp_t

W_tot_err

1

Time (s)

52

Figure 28 - Overall Energy Behavior with PID Regulator (Joule)

Figure 29 - Difference Energy with PID Regulator (Joule)

0 1 2 3 4 5 6190

200

210

220

230

240

250

260

Time

0 1 2 3 4 5 6-6

-4

-2

0

2

4

6

Time

Time (s)

Time (s)

53

4.5 - Fourth model Mega-Watt System

The model presented and studied in previous sections was a kW power system: in this

chapter the analysis and simulation results will be proven on a MW power system.

The MW power system requires only changing the limitations on the differential

voltage available: as much as the power increases, as much the differential voltage,

used to control the energy stored in the system, has to increase.

The control system scheme remains exactly the same, and will be proven to be

reliable and tightly dependent with system parameters: however, an important

consideration has to be deepened about system project.

Even if not compromising stability, plays a fundamental role in the operation of

the system: the sizing of this parameter has to take in consideration the voltage ripple

that its considered to be acceptable. When considering the previous simulations (the

kW power system) was big enough in order to minimize voltage ripples in the

upper and lower modules: considering a MW power system, it is important to discuss

the size of the capacitor in order to understand the relationship between this parameter

and control constraints.

4.5.1 - Capacitance - Voltage Ripple Relationship

Starting from voltage derivate equations in (13), here rewritten for convenience,

it is possible to find a relationship between voltage and arm capacitance. Considering

only the upper arm voltage (but same results would be obtained considering lower

arm voltage), it is possible to substitute currents with their behavior over time

For the differential current, it is possible to consider only the DC component: this

component is used to maintain the capacitor voltage to a constant value.

It is possible to integrate the voltage equation in the positive half period of the output

current, yielding

54

[ ]

where modulation index con be considered as

with the hypothesis that

(41)

Substituting (40) and (41) in (39) we obtain

[

]

(42)

[

[ ]

[ ] ]

[

]

Finally a relationship between and voltage ripple is found as

[

] [

]

With this equation it is possible to understand the system operation and thus to size

properly the capacitance of the arm, once assigned output current and calculated the

DC component of differential current, in order to satisfy voltage ripple constraints.

55

4.5.2 - Simulation Results

Parameters of Mega-Watt power system are listed in Tab. 2.

Tab. 1 List of system parameters

The first simulation shown in the report shows the steady state operating conditions of

the MW power converter: as expected, the general behavior of the converter is

unchanged in comparison with the kW power converter.

The only change can be seen in the order of magnitude of variables observed. Figs. 30

and 31 show total energy and balance energy waveforms.

Figure 30 - Overall Energy (Joule) Steady State Waveform

0 1 2 3 4 5 61.98

1.985

1.99

1.995

2

2.005

2.01

2.015x 10

6

TimeTime (s)

56

Figure 31 - Difference Between Upper and Lower Arm Energy (Joule)

Figure 32 - Differential Current (A) in Steady State Conditions

0 1 2 3 4 5 6-6

-5

-4

-3

-2

-1

0

1

2

3x 10

4

Time

0 1 2 3 4 5 6260

280

300

320

340

360

380

400

420

Time

Time (s)

Time (s)

57

In Fig. 32 differential current behavior is shown: continuous component increased

proportionally to output current and line voltage, in order to balance output power

increase. The alternate component remains limited and guarantees stability in upper

and lower arm voltage. It is possible to notice the DC component, around 340 A, to

balance output power and the AC component to balance Upper and Lower voltages.

Fig. 33 instead shows upper and lower arm voltages: as deepened in previous section,

oscillations of these voltages are related to capacitors designed for the converter. In

order to reduce the ripple it would be necessary to increase the capacitor in each sub-

module: however, with the actual design and control tuning, voltage ripple is less than

1%.

Figure 33 Upper (Blue) and Lower (Green) Arm Voltages (V) in Steady State

Conditions

The second simulation aims to test dynamic response of the system, in terms of step

variation of the overall energy stored in the converter. As in previous models, this

kind of simulation is not representative of a particular operating condition: it is

however the best way to test control stability and performances of the total energy

loop.

Even with a 50% change of the overall energy reference, the loop response respects

all requirements: rising time is around 500 ms and there is no overshoot or relevant

oscillations around the new steady state condition, as represented in Fig. 34.

0 1 2 3 4 5 61.96

1.97

1.98

1.99

2

2.01

2.02

2.03

2.04x 10

4

TimeTime (s)

58

The influence of the overall energy loop on the balancing control loop is almost

negligible, due to the frequency decoupling performed with control loops, and can be

seen in Fig. 35.

From Fig. 36, it can be noted that differential current waveform respects all

expectations: there is a short transient between initial and final steady state conditions

in order to accomplish the overall energy reference change

The same dynamic response can be seen in upper and lower arm voltages as

represented in Fig. 37.

Figure 34 - Overall Energy (Joule) Step Response with a 50% Change of the Overall

Energy Reference

0 1 2 3 4 5 61.8

2

2.2

2.4

2.6

2.8

3

3.2x 10

6

TimeTime (s)

59

Figure 35 - Difference Between Upper and Lower Arm Energy (Joule) with a 50%

Change of the Overall Energy Reference

Figure 36 - Differential Current (A) Behavior with a 50% Change of the Overall Energy

0 1 2 3 4 5 6-6

-5

-4

-3

-2

-1

0

1

2

3

4x 10

4

Time

0 1 2 3 4 5 6250

300

350

400

450

500

550

Time

Time (s)

Time (s)

60

Figure 37 - Upper (Blue) and Lower (Green) Arm Voltages (V) with a 50% Change of

the Overall Energy

4.5.3 - Simulation Results: Sub-Modules Failure Mode

In order to properly test also the balancing loop and to verify the coupling with

overall energy loop further simulations are necessary: the initial condition of

capacitors is set so that the system starts from an unbalanced condition. Thus, it will

be possible to understand if the decoupling is possible in both directions of

interaction: previous simulations showed that overall energy loop slightly influences

balancing loop, but it is not possible to conclude the same for the opposite coupling.

This initial unbalance condition is related to a fault condition, where a certain number

of broken sub-modules are bypassed: in order to remain in a fail-safe region, the

control has to be fast and reliable, reaching the steady state condition without

overshoots or oscillations.

Fig. 38 shows the overall energy behavior: starting from an unbalanced initial

condition, the interaction between balancing loop and overall energy loop is not

negligible.

0 1 2 3 4 5 61.9

2

2.1

2.2

2.3

2.4

2.5x 10

4

TimeTime (s)

61

Figure 38 - Overall Energy (Joule): Response to Unbalanced Initial Conditions

The balancing loop acts slowly and takes a longer transient to set to zero the error, as

can be noted in Fig. 39. The overall energy loop instead acts immediately to reach the

steady-state reference value. As a consequence, the unbalanced initial condition leads

to dangerous operation due to an important overshoot of the overall energy stored in

capacitors, as clearly emphasized in Fig. 38.

The differential current flowing through the leg is the same for both upper and lower

sub-modules: even if only one of the arms needs to be charged, the differential current

will charge both of them, leading to a condition where the overall energy of the

system overshoots greatly the reference value. This can be clearly understood

analyzing the upper and lower arm voltage waveforms, shown in Fig. 40. It is

possible to notice the overshoot of booth voltages, due to the same charging current.

0 1 2 3 4 5 61

1.5

2

2.5

3

3.5

4x 10

6

TimeTime (s)

62

Figure 39 - Difference between Upper and Lower Arm Energy (Joule): System Response

to Unbalanced Initial Conditions

Figure 40 - Upper (Blue) and Lower (Green) Arm Voltages (V): System Response to

Unbalanced Initial Conditions

0 1 2 3 4 5 6-8

-7

-6

-5

-4

-3

-2

-1

0

1x 10

5

Time

0 1 2 3 4 5 61

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3x 10

4

Time

Time (s)

Time (s)

63

The balancing loop acts as a disturbance for the overall energy loop, trying to reduce

the unbalance with the same charging current and thus slowing down the dynamic

response of voltages.

In order to reach the overall energy reference, control loop requires a high value of

differential current, which instantaneously charges both upper and lower capacitors.

The problem is mainly caused by the fast response of the overall energy loop: the

differential current required, in order to set to zero the error, charges both upper and

lower arm sub-modules, leading to a non-acceptable overshoot.

Thus an improvement in the control strategy is required, taking into account that the

differential current will charge anyway both upper and lower sub-modules.

In the event that one could ignore output variables behavior during the transient, it

would be easy to eliminate the overshoot: the already charged arm would be

bypassed, eluding the problem shown in previous simulations. But, as the tracking of

output variable references is imposed, no significant improvement can be obtained

from low level control.

Thus, the best solution is to work directly on the differential current: this approach

will permit to guarantee output variables to follow reference (with just a brief

transient) and reduce significantly overshoot in the energy response.

It is important to note that a significant overshoot reduction cannot be achieved

retuning the parameters of regulators; this because the small capacitors used in sub-

modules have a charging dynamic too fast for preventing completely overshoots by

acting on the converter regulators .

In this thesis, parameters will not be changed, but instead an improved control scheme

will be investigated and proposed. In order to prevent energy and voltage overshoots,

differential current is monitored and controlled. As it is not possible to directly control

this current, thus a feed-back-like structure is realized on the differential voltage loop

that influences overall energy loop.

If differential current overcomes a safe range, a proportional action acts in order to

decrease the differential voltage contribution and thus limit differential current. In

Fig. 41 the scheme representing the principle of operation is shown. Violet blocks are

used to compare differential current with an equivalent saturated current (saturation is

imposed to remain in a safe range of operation) and a proportional controller is then

imposed to the error.

Figs. 42 and 44 show the improvement of energy and arm voltages behavior: the

differential current control reduces arm voltages overshoots, and thus overall energy

overshoot. Actually, uncharged sub-modules reach voltage reference smoothly,

without overshoots: the already charged arm has however a small overshoot, due to

charging current. The behavior of the converter is now acceptable, and the overall

energy overshoot is less than 10%. Balancing of energy behavior remains almost the

same, compared to previous simulations and it is shown in Fig. 43.

64

Figure 41 - Improved Control Strategy

65

Figure 42 - Overall Energy (Joule): System response from an unbalanced initial

condition with the new regulator

Figure 43 - Difference between Upper and Lower Arm Energy (Joule): System response

from an unbalanced initial condition with new regulator

0 1 2 3 4 5 61.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2x 10

6

Time

0 1 2 3 4 5 6-8

-7

-6

-5

-4

-3

-2

-1

0

1x 10

5

Time

Time (s)

Time (s)

66

Figure 44 - Upper (Blue) and Lower (Green) Arm Voltages (V): System response from

an unbalanced initial condition with the new regulator

0 1 2 3 4 5 61

1.2

1.4

1.6

1.8

2

2.2

2.4x 10

4

TimeTime (s)

67

4.5.4 - Simulation Results: LVRT

Last simulations shown in this thesis are related to Low Voltage Ride Through issue:

in order to simulate this operating condition, grid voltage is set to zero for 200 ms

as represented in Fig. 45.

Figure 45 Grid Voltage (V) during LVRT

The aim of this simulation is to see the energy behavior of the system; internal

transient and current ripples need a more precise and focused modeling approach, but

it is not in the scope of this thesis. What the simulation is supposed to proof is the

reliability and safety of energy control system in faulty operating conditions.

It is plausible to expect a transient before the system reaches a new fail steady-state:

after this condition, a new transient will lead the system back to the healthy operating

conditions.

Actually, the system behavior fulfills expectations: as shown in Fig. 46, the overall

energy is stable and has a small transient, leading to a steady-state condition.

Balancing control too, is able to maintain upper and lower arm voltages to the same

desired value, as illustrated in Fig. 47.

Fig. 48 and 49 show the waveforms of capacitor voltages and differential current,

respectively. The transient during LVRT is coherent with what expected. Differential

current mean value is zero during the fault as the output power drops to zero. The

2.8 2.9 3 3.1 3.2 3.3 3.4

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

TimeTime (s)

68

alternate component instead remains almost unchanged, in order to maintain the

balance between upper and lower arm voltages.

Figure 46 - Overall Energy (Joule): Behavior in LVRT condition

Figure 47 - Difference between Upper and Lower Arm Energy (Joule): Behavior in

LVRT condition

0 1 2 3 4 5 61.9

1.92

1.94

1.96

1.98

2

2.02

2.04

2.06x 10

6

Time

0 1 2 3 4 5 6-8

-6

-4

-2

0

2

4

6x 10

4

Time

Time (s)

Time (s)

69

Figure 48 Upper (Blue) and Lower (Green) Arm Voltages (V): Behavior in LVRT

condition

Figure 49 - Differential Current (A): Behavior in LVRT condition

0 1 2 3 4 5 61.92

1.94

1.96

1.98

2

2.02

2.04

2.06x 10

4

Time

0 1 2 3 4 5 6-200

-100

0

100

200

300

400

500

Time

Time (s)

Time (s)

70

71

Chapter V

5.1 Motivation for a new modelling approach

From results obtained and showed in previous chapter, it possible to conclude that

linear control behaves properly in steady state condition and in certain dynamic

operation condition.

However, as underlined in Section 3.3, it is really hard to investigate advanced and

robust control strategy, due to high non linearity in model equations.

Even if the linear control strategy gives a satisfying response, parameters changing,

failure modes, fast dynamic requirements scenarios may introduce problems in the

stability of the system: thus, these possibilities call for a deepening in different control

approaches (for instance adaptive, robust, feedback linearization, optimal control etc).

In order to facilitate these studies, a new model approach here is proposed: the aim of

this modelling approach is to obtain more linear equations: even if it is not possible

to derive a completely linear model, it is desirable to apply advance control

techniques to a simpler set of equations.

5.2 Modelling Principles and Equations

A new simplified schematic of the MMC leg is proposed and shown in Fig: 50: grid is

not represented because not strictly necessary in this analysis, but must be introduced

to build a simulation model.

Figure 50 - New Simplified MMC Leg Model

+EDC

VO

iO

iP

iN

VN

VP

EN

EP

CN

CP

SMs

P

SMs

N

Zp

ZN

72

With reference to Fig 50, it is possible to write voltage loop and current equations

following Kirchhoffs laws.

Defining Sp and Sn as modulation indexes, respectively of upper and lower arms, it is

possible to write:

It is also possible to define dynamic equations for equivalent capacitors voltages,

depending on modulation indexes:

It is possible to assume that output current reference is assigned: the problem of

controlling this current has a consequence in arm currents control.

These arm currents are supposed to maintain the overall energy to a desired value, to

balance the difference between upper and lower arm energy and to guarantee output

current to follow assigned set-point.

Thus, it is possible to write equations (53) and (54), in which the differential current is

introduced:

From (53) and (54), it is possible to calculate upper and lower arm current references:

73

The problem can be easily solved if differential current reference is assigned: as

mentioned before, this quantity has to be determined in order to maintain sub-module

capacitors charged and balanced.

Using equations (55) and (56) it is possible to calculate the arm current references,

then it is possible to create the current control loops as represented in Fig. 51.

Figure 51 - Currents Control Loops

From equations (49) and (50) it is then possible to calculate modulation indexes,

whose expressions are given in (57) and (58):

In order to find differential current reference, it is necessary to write and analyze

energy equations of MMC leg: instead of writing upper and lower energy equations,

total energy and unbalance energy equations are suggested.

Lets consider WT and WD as total energy and difference energy between upper and

lower arms, respectively:

74

Introducing capacitor voltages and currents references, then equations (61) and (62)

are obtained:

It is possible to assume that voltage drop contribution created by currents on arm

impedance is negligible in comparison with capacitors voltage contribution: in order

to find a dynamic relationship between energy variations and variables available to

control MMC, equations (63) and (64) are introduced.

It is necessary to point out differential current contribution: thus, substituting upper

and lower arm currents with their reference expressions, i.e. equations (55) and (56),

yields to

(

)

(

)

If output current and voltage are periodical functions, with period T0 it is possible to

integrate equations (65) and (66), leading to

(

)

75

(

)

These equations show clearly differential current contribution in system energy

dynamic operation: total energy WT depends form differential current mean value,

WD instead depends form the alternate component of differential current having the

same frequency as output voltage.

These considerations can be summarized with the following scheme, Fig. 52.

Figure 52 Energy Control Scheme Diagram

5.3 Control Proposal

In this Section, control scheme previously described is explained extensively.

Compared with the control approach of Chapter III, used for simulation results in

Chapter IV, this new approach provides a cascade structure.

Two different loops are realized, an energy loop and a differential current loop:

energy loop provides a differential current reference, which is tracked by the current

control loop.

Energy loop is composed of overall energy control and balancing control.

Current loop is composed of upper current control and lower current control.

The complete control scheme is shown in Fig. 53.

76

Figure 53 - Control Scheme for new Modeling Approach

77

Following equations (46) and (47), current control loop is pretty easy to be tuned:

actually, between upper and lower arm voltages and arm currents only an R-L low

pass filter is present. Then, through equations (49) and (50), modulation indexes, real

system input, can be calculated.

Once control loop is tuned, it is possible to work on energy loop: using equations (65)

and (66), it is possible to control total energy and balancing dynamics. Thus, an

integrator is not necessary to set to zero total energy error and balancing error (i.e. an

integrator is intrinsically present in the system).

Control suggested and shown in Fig. 53 includes PD controller: this control structure

is again based on a frequency decoupling, where balancing loop is tuned to be slower

than total energy loop.

Simulation parameters chosen are the same used in the Mega-Watt system discussed

in Section 4.5.

In Figs. 54, 55 and 56, the simulation of a steady state condition is shown: the initial

transient is due to equation structure. A differential current derivative equation is not

present in the model, thus it is not possible to impose the initial condition.

It is however possible to see that after 2 s a steady state condition is reached without

overshoot or oscillation.

Figure 54 - Upper and Lower Arm Capacitor Voltages

0 1 2 3 4 5 61.94

1.96

1.98

2

2.02x 10

4 Ep

0 1 2 3 4 5 61.94

1.96

1.98

2

2.02x 10

4

Time

En

78

Figure 55 - Differential Current Transient (A)

Figure 56 - Output Current (A) and Output Voltage (V)

0 1 2 3 4 5 6-200

0

200

400

600

800

1000

Time

Id_ref

0 1 2 3 4 5 6-2000

-1000

0

1000

2000Io

0 1 2 3 4 5 60

0.5

1

1.5

2x 10

4

Time

Vo

79

Further simulations, concerning dynamic behaviour of the system, will be carried out

in the near future: however, it was considered important to show a simple simulation

introducing the validity of the approach.

A comparison with model proposed in [8] (that has been used in the beginning of this

thesis to deepen system operation and control strategies) will also be developed: as an

introduction, next Section will briefly compare the equations of the two models in

order to propose future control possibilities.

5.4 Future Works

Besides to basic control strategy described in previous paragraph, new modeling

approach gives a set of equations which are easier to be used in order to deepen

advanced control strategies.

It is possible to compare energy equations between the new proposed model and the

model described in [8]:

( )

(

)

(

)

(

)

Neglecting notation differences, the high non-linearity of equations (34) and (35) is

smoothed considerably in equations (65) and (66).

Total energy in equations (34) is controlled through differential current, which is a

square non-linear input for the system (see Section3.3): in equation (65) instead, the

input is linear because the differential current is multiplying the DC voltage, which

can be considered constant.

A similar consideration may be done about balancing equations: equation (35) is

highly non-linear for input variables (differential voltage and differential current),

instead equation (66) has a component of the input which is still linear and can be

used to implement advanced control strategies.

Equations (34) and (35) give few chances to develop advanced control techniques,

due to their intrinsic non-linear structure.

80

Equations (65) and (66) instead, make it easier to define advanced control strategies

based on model inversion, feed-forward actions, and feed-back linearization.

All these possibilities will be investigated in near future and their functionality and

performances will be compared with standard linear controllers already implemented

and discussed in this work.

81

Chapter VI Conclusions

The aim of this project was the analysis of a Modular Multilevel Converter (MMC)

for wind farm applications and the development of a control scheme to monitor the

energy behavior.

The analysis was based on the use of a simplified circuit, constituted by a single leg of

the converter, where all the modules in each arm were represented by a single variable

voltage source. The circuit model was derived as a system of differential equations,

used for analyzing both the steady state and dynamic behavior of the MMC, from

voltages and thus energy point of view.

Preliminary analysis was carried out following the modeling approach proposed in

[8]. Using this model, the system behavior has been studied and a possible energy

control scheme has been developed. The numerical simulations have shown that the

system is operating correctly under steady-state and transient operating conditions,

except for initial conditions with unbalanced capacitor voltages. To reduce the large

voltage overshoots due to this unbalanced initial condition, an improved control

scheme has been developed.

In Chapter V, a new modeling approach was proposed, aiming to define a set of

equations more suitable for advanced control implementation.

With the new modeling approach a significant contribution to control issues will be

possible: in the near future, a comparison between the new modeling approach and the

one proposed in [8] will be investigated.

New control structures will also be developed, in order to accomplish all dynamic

requirements required by the particular application, i.e. to comply wi